I am also mildly claustrophobic and you just reminded me of my 2015 MS Green experience which is making me question if I really want to do Orange with my girls this Summer because I know they would love it and I would feel uncomfortable with them going on their own.
What, exactly, concerns you about them for it on their own? If you don't want them waiting in line or exiting without you, you can absolutely stay with them in line and use the chicken exit to wait for them.
If it's them being in the vehicle with strangers, I personally don't consider that dangerous, but I wouldn't dream of indicating it's wrong to feel that way. But you can absolutely ask the loaded if they can have their own pod.
I know people have said to just look straight ahead, but I find I can move my eyes without moving my head inside the pod. Anywhere, really, just like most people

.
EDIT: Oh, and make sure you push that button when it lights up. It is very important.
Still? Somebody upthread mentioned that if you don't push your button, the vehicle crashes. It's how I discovered I can glance sideways

. My first ride, way back when it was all just the intense level, not everybody in my crew it was interactive. I think I had to control three operations.
Subsequent rides, the vehicle hasn't always been fully staffed. Again wanting to avoid a crash, I reacted to multiple instructions.
Or g-forces.
My wife doesn't get motion sick and isn't claustrophic but has had some facial surgery and can't do the g-forces. She will do the weenie side on occasion (I never remember which color is which).
Green for
good-to-go,
orange for
oh-oh-oh-my-goodness!